Results 61 to 70 of about 271 (247)

A Unifying Approach to Self‐Organizing Systems Interacting via Conservation Laws

Advanced Intelligent Discovery, EarlyView.
The article develops a unified way to model and analyze self‐organizing systems whose interactions are constrained by conservation laws. It represents physical/biological/engineered networks as graphs and builds projection operators (from incidence/cycle structure) that enforce those constraints and decompose network variables into constrained versus ...
F. Barrows, G. Zhang, S. Anand, Z. Chen, J. Lin, A. Desai, S. Martiniani, F. Caravelli   +7 more
wiley   +1 more source

Representation of Integral Formulas for the Extended Quaternions on Clifford Analysis

Mathematics
This work addresses a significant gap in the existing literature by developing integral representation formulas for extended quaternion-valued functions within the framework of Clifford analysis. While classical Cauchy-type and Borel–Pompeiu formulas are
Ji Eun Kim
doaj   +1 more source

Quaternion constituents of group algebras [PDF]

Proceedings of the American Mathematical Society, 1971
In this paper it is shown that each quaternion division algebra central over the rationals appears as a division ring constituent of some rational group algebra.
openaire   +2 more sources

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

Hyperpolyadic Structures

Mathematics
We introduce a new class of division algebras, the hyperpolyadic algebras, which correspond to the binary division algebras R, C, H, O without considering new elements. First, we use the matrix polyadization procedure proposed earlier which increases the
Steven Duplij
doaj   +1 more source

Pre‐Curved Everting Robots With Embedded Steering Intelligence Fabricated by CO2 Laser Welding

Advanced Intelligent Systems, EarlyView.
Design and experimental demonstration of a laser welded growing robot for anatomically guided navigation. The robot follows an aortic arch phantom entering the branchiocephalic branch through steering by design. The figure shows the physical phantom setup, CAD defined weld geometry and full robot eversion.
Brandon Saldarriaga, Panagiotis Kalozoumis, Panagiotis Vartholomeos, Carlo Seneci, Kawal Rhode, Christos Bergeles   +5 more
wiley   +1 more source

Programmable Flocks: Hierarchical Swarm Control via Dynamic Parameter Injection

Advanced Intelligent Systems, EarlyView.
We present a method for the control of robot swarms which allows the shaping and the translation of patterns of simple robots (“smart particles”), using two types of devices. These two types represent a hierarchy: a larger group of simple, oblivious robots (which we call the workers) that is governed by simple local attraction forces and a smaller ...
Vivek Shankar Varadharajan, Giovanni Beltrame   +1 more
wiley   +1 more source

Designing Wire Mazes for Replicating Natural Echoes to Study Bat Biosonar Function

Advanced Intelligent Systems, EarlyView.
A validated framework combining efficient physical modeling (multiple scattering model) and deep learning is presented to guide wire‐maze design for bat biosonar studies. This approach rapidly generates large datasets to test acoustic distinguishability among wire arrangements.
Chunlin Jia, Gengkai Hu, Boo Cheong Khoo, Rolf Müller   +3 more
wiley   +1 more source

Generalized Pauli Fibonacci Polynomial Quaternions

Axioms
Since Hamilton proposed quaternions as a system of numbers that does not satisfy the ordinary commutative rule of multiplication, quaternion algebras have played an important role in many mathematical and physical studies.
Bahadır Yılmaz, Nazmiye Gönül Bilgin, Yüksel Soykan   +2 more
doaj   +1 more source

Orders in quaternion algebras

, 1989
The authors define and study the arithmetic of special orders in quaternion division algebras over number fields. Special orders are analogous to orders of the form \(\left( \begin{matrix} Z\\ NZ\end{matrix} \begin{matrix} Z\\ Z\end{matrix} \right)\) in \(Mat(2,{\mathbb{Q}}_ p)\) and include maximal and Eichler orders as special cases.
Hijikata, H., Pizer, A., Shemanske, T.
openaire   +1 more source